Multivariable Integral Solver
Result: -
Understanding Multivariable Integration
Double Integrals
A double integral represents the volume under a surface over a region in the xy-plane:
∫∫R f(x,y) dA = ∫ab ∫cd f(x,y) dy dx
- Used to calculate area, volume, mass, and center of mass
- Order of integration matters for efficiency
- Can be evaluated using iterated integrals
Triple Integrals
Triple integrals extend to three dimensions and are used for:
- Volume calculations in 3D space
- Mass of three-dimensional objects
- Gravitational fields
- Fluid flow analysis